A playground is on the flat roof of a city school, 6.00 m above the street below (Fig. P3.34). The vertical wall of the building is h = 7.00 m high, to form a 1-m-high railing around the playground. A ball has fallen to the street below, and a passerby returns it by launching it at an angle of θ = 53.0° above the horizontal at a point d = 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall. (a) Find the speed at which the ball was launched. (b) Find the vertical distance by which the ball clears the wall. (c) Find the horizontal distance from the wall to the point on the roof where the ball lands.

For safety reasons, park rangers decide to start an avalanche on a mountain slope.  They fire an artillery shell at an angle of 520 above the horizontal with an initial speed of 295 m/s.  Thirty seconds later they see the explosion.  What is the x coordinates of the shell where it explodes, relative to the firing point?

Consider a projectile being launched with an initial speed of 43 m/s at a variety of initial angles. Refer to the figure. What is the range, in meters, of the projectile if it is launched at an angle of θ1 = 79.7°?  What is the range, in meters, of the projectile if it is launched at an angle of θ2 = 40.5°?  What is the range, in meters, of the projectile if it is launched at an angle of θ3 = 90 − 79.7°, the complement of θ1?

A baseball is thrown at an angle θ = 22° above the horizontal with an initial vertical velocity v0y = 13.5 m/s. Use a Cartesian coordinate system with the origin at the baseball's initial position. Calculate the initial horizontal velocity component, v0x in m/s.

How do you solve this? I've got 2/3 so far

You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v at an angle 0 with respect to the horizontal. Let the building be 54.0 m tall, the initial horizontal velocity be 9.10 m/s, and the initial vertical velocity be 10.5 m/s. Choose your coordinates such that the positive y-axis is upward, and the x-axis is to the right, and the origin is at the point where the ball is released. (a) With these choices, find the ball's maximum height above the ground and the time it takes to reach the maximum height. maximum height above ground time to reach maximum height (b) Repeat your calculations choosing the origin at the base of the building. maximum height above ground time to reach maximum height

In my homework, I am asked to derive an equation for V0.   The homework question is as follows: A howitzer fires a shell with a velocity of v0 at an angle Θ above the horizontal. The howitzer is on a plateau and the shell lands down in the plain below, a vertical distance d below the plateau and a horizontal distance L from where the howitzer is. Derive an expression for the magnitude of the initial velocity, V0, as a function of d, L, g, and Θ.   Any help would be appreciated as I have worked on this problem for quite a while and I am not making progress.

2 M S F2 7. The captain of a small plane starts his journey by proceeding west. The speed of the plane with respect to still air is 170 km/h. A sudden south wind starts to blow at a constant speed of 87.5 km/h. What is the speed of the plane relative to the ground if no action is taken by the pilot? km/h 3 8. b) As seen by people on the ground, what is the angle made between the direction of motion of the plane with repect to the west? 9. c) At what angle with respect to the west must the pilot head his plane in order for it to proceed west as seen by the people on the ground? E 80 F3 D $ 4 F4 R F % O 5 F5 T G 6 MacBook Air IS Y & 7 H F7 U * 8 J DII FB ( 9 K F10 L P F12

Snowballs are thrown with a speed of 19 m/s from a roof 7.0 m above the ground. Snowball A is thrown horizontally; snowball B is thrown in a direction 35° above the horizontal. Find the direction of motion (that is, the angle of the velocity vector) of each of the two snowballs just before they land.

Hole number 7 at Pebble Beach golf course is one of the shortest championship holes in the world. The hole is only 100m away from the tee, and it is also 12m lower. Champion golfer Shooter McGavin hits a 9-iron at an angle of 50◦ with respect to the horizontal, and lands the ball right in the hole. Assume there is no wind or air resistance, and g = 9.8 m/s^2. (sin 50◦ = 0.766, cos 50◦ = 0.643, tan 50◦ = 1.19, sin 45◦ = 0.707, cos 45◦ = 0.707, tan 45◦ = 1.00). What is the initial velocity of the ball? How long was the ball in the air? What was the maximum height? If Shooter had misjudged the hole, and hit the ball with the same velocity but at an angle of 45◦ instead, by how much would he have overshot the hole?